(image by Cowdery and Challas, featured in June 2009 Mathematics Magazine)

This is a reading and viewing list for a small group of people who are working to learn these topics. Anyone is welcome to use it, of course.

• Algebraic groups and representation theory
  • Humphreys, Linear Algebraic Groups (Springer)
• Toric varieties
  • Cox, Little, Schenck, Toric varieties (AMS)
• Tropical geometry
  • Draft of the textbook Introduction to Tropical Geometry by Maclagan and Sturmfels
  • Videos from the introductory workshop on Tropical Geometry at the Mathematical Sciences Research Institute in August 2009
• Spherical varieties
  • Perrin, Introduction to spherical varieties
  • Perrin, On the geometry of spherical varieties
  • Pezzini, Lectures on spherical and wonderful varieties
  • Pasquier, Introduction to spherical varieties and description of special classes of spherical varieties
• Associated convex bodies
  • Lazarsfeld and Mustaţă, Convex Bodies Associated to Linear Series, (arXiv:0805.4559)
  • Kaveh and Khovanskii, Convex bodies associated to actions of reductive groups, (arXiv:1001.4830)
  • Kiritchenko, Smirnov, Timorin, Schubert calculus and Gelfand-Zetlin polytopes, (arXiv: 1101.0278)
  • Miller, Okounkov Bodies of Borel Orbit Closures in Wonderful Group Compactifications, Ph.D. dissertation at the Ohio State University, 2014
  • Videos from the workshop Convex Bodies and Representation Theory at the Banff International Research Station in February 2014